Number theory problems:

#18. (a) Prove that there are infinitely many primitive Pythagorean triples x, y, z with z = x + 1. (Hint: If n is a positive integer, consider the triple 2n2 + 2n, 2n + 1, 2n2 + 2n + 1.) (b) Prove that every primitive Pythagorean triple x, y, z with z = x + 1 is of the form given in the hint of part (a) above